If the app being free for a day is their choice then yes, they will pay 20% of the minimum list price in that period (as 0.2 x List will be more than 0.7 x Free).
If you dare give your app away for a day or allow another marketplace to do so, and sell your app via Amazon now or at any time in the future, you must permanently reduce your minimum list price at Amazon to $0.00 meaning that from this point they could give your app away for free as often as they like and give you nothing (0.2x0.00 == 0.7x0.00 == 0.00).
Essentially this means you can't give an exclusive offer to anyone other than Amazon, including via your own site if I'm understanding correctly, without also giving Amazon the option of the same offer (meaning is isn't much of an exclusive) and not just now: they have the option of running the offer when-ever and how often they like now and at any time in the future.
If you dare give your app away for a day or allow another marketplace to do so, and sell your app via Amazon now or at any time in the future, you must permanently reduce your minimum list price at Amazon to $0.00 meaning that from this point they could give your app away for free as often as they like and give you nothing (0.2x0.00 == 0.7x0.00 == 0.00).
Essentially this means you can't give an exclusive offer to anyone other than Amazon, including via your own site if I'm understanding correctly, without also giving Amazon the option of the same offer (meaning is isn't much of an exclusive) and not just now: they have the option of running the offer when-ever and how often they like now and at any time in the future.